Dynamic Programming: An overview

The mathematical theory of dynamic programming as a means of solving dynamic optimization problems dates to the early contributions of Bellman [1957] and Bertsekas [1976]. For economists, the contributions of Sargent [1987] and Stokey-Lucas [1989] provide a valuable bridge to this literature. 2 Indirect Utility Intuitively, the approach of dynamic programming can be understood by recalling the theme of indirect utility from basic static consumer theory or a reduced form profit function generated by the optimization of a firm. This reduced form representations of payoffs summarizes information about the optimized value of the choice problems faced by households and firms. As we shall see, the theory of dynamic programming uses this insight in a dynamic context. 2.1 Consumers Consumer choice theory focuses on households who solve: V (I, p) = max